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This is a methodological critique of research by the Best Practice in Grouping Students (BPGS) project claiming teacher bias in allocating students to first‐year secondary school mathematics teaching sets (British Educational Research Journal, 45(4), 873–879). The research assumes that bias could be shown by non‐random relationships between 'misallocations' to sets and memberships of gender, ethnic and/or socio‐economic subgroups. This paper questions the authors' prescriptions for correct set placements and demonstrates two ways in which non‐random relationships between subgroup memberships and (alleged) misplacements could be generated despite all students with similar scores within a school being given the same chance of a set position deemed correct by the researchers. It suggests that the BPGS project results are largely artefacts of their evaluation approach. No claim is made herein that teacher bias plays no part in set allocation, merely that, if it does, the approach by Connolly et al. could not evidence it. A lesson from the critique is that, before drawing inferences from data aggregated from diverse clusters, it is wise for researchers to investigate the way the data are generated at source and patterned by aggregation. [ABSTRACT FROM AUTHOR]

Background: Eye movement modelling examples (EMME) are demonstrations in which learners' not only see a model's (e.g., a teacher's) task performance on a computer screen (as in regular video examples) but also the model's eye movements (represented as moving coloured dots overlaid on the screen). Thereby EMME help guide learners' attention towards the relevant information and can model cognitive strategies which are otherwise unobservable for learners. Objectives: This study investigated whether EMME can help to learn deductive reasoning strategies and how the presence/absence of a teacher's verbal explanation affects learning from EMME. Methods: Secondary education students (N = 137) were randomly assigned to study video examples under one of four conditions in a 2 (EMME: yes/no) x 2 (verbal explanations: yes/no) between‐subjects design. Results and Conclusions: Results revealed only a beneficial effect of the presence of verbal explanations on performance on the practice problems, but no pretest‐to‐posttest learning gains. Implications: Seeing the teacher's eye movements does not appear to enhance learning of deductive reasoning. The presence/absence of the teacher's verbal explanation does not seem to affect learning deductive reasoning. Lay Description: What is currently known about the subject matter?: Eye movement modelling examples (EMME) are demonstrations in which learners not only see a teacher's task execution on a computer screen (as in video examples) but also the teacher's eye movements.The eye movements in EMME were visualized as moving coloured dots overlaid on the screen recording.EMME help direct attention to relevant information and enhance learning; it is not yet known if this also applies to reasoning problems.It is unknown if and how presence/absence of a teacher's verbal explanation affects learning from EMME. What our paper adds to this?: Secondary education students watched EMME or regular video examples with/without a teacher's verbal explanation.The examples demonstrated how to solve deductive reasoning problems (adapted version of the Mastermind game).Performance and learning gains were examined and revealed no differences between conditions. The implications of study findings for practitioners: Seeing the teacher's eye movements does not appear to enhance learning of deductive reasoning.The presence/absence of the teacher's verbal explanation does not seem to affect learning deductive reasoning. [ABSTRACT FROM AUTHOR]

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a) MS positioning across research; (b) historical trends of school‐based MS research; and (c) orientations of school‐based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p‐12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research. [ABSTRACT FROM AUTHOR]

Interim assessments have been defined variously in different contexts and can be used for predictive purposes or instructional purposes. In this paper, we present results from a study where we evaluated reporting needs for interim assessments designed for instructional purposes and intended to be used at the end of defined curriculum units. Results from such unit assessments should help teachers determine gaps in student understanding and inform ongoing instructional decision‐making. Our goal was to determine if learning progressions (LPs) could serve as the cognitive lens through which teachers can evaluate how their students' understanding of key constructs improves through periodic unit assessments. Therefore, we used the LP framework in mathematics and the key practices (KP) framework for English language arts (ELA) to design preliminary teacher report mock‐ups for these unit assessments. Within a utilization‐oriented evaluation framework, we conducted six needs‐assessment focus groups with elementary and middle school mathematics (n = 12) and ELA (n = 11) teachers to specifically evaluate the extent to which they find results presented within the LP and KP frameworks understandable and useful for their instructional practice. Results from the focus groups show teachers' overall needs for types of information sought from unit assessment reports, the extent to which teachers are familiar with the LP and KP frameworks, their interpretations (including confusions) of the information presented in the preliminary mock‐ups, and their additional needs for reports from unit assessments to be instructionally useful. Report Number: RR‐21‐08 [ABSTRACT FROM AUTHOR]

Background: Building on the Realistic Accuracy Model, this paper explores whether it is easier for teachers to assess the achievement of some students than others. Accordingly, we suggest that certain individual characteristics of students, such as extraversion, academic self‐efficacy, and conscientiousness, may guide teachers' evaluations of student achievement, resulting in more appropriate judgements and a stronger alignment of assigned grades with students' actual achievement level (as measured using standardized tests). Aims: We examine whether extraversion, academic self‐efficacy, and conscientiousness moderate the relations between teacher‐assigned grades and students' standardized test scores in mathematics. Sample: This study uses a representative sample of N = 5,919 seventh‐grade students in Germany (48.8% girls; mean age: M = 12.5, SD = 0.62) who participated in a national, large‐scale assessment focusing on students' academic development. Methods: We specified structural equation models to examine the inter‐relations of teacher‐assigned grades with students' standardized test scores in mathematics, Big Five personality traits, and academic self‐efficacy, while controlling for students' socioeconomic status, gender, and age. Results: The correlation between teacher‐assigned grades and standardized test scores in mathematics was r =.40. Teacher‐assigned grades more closely related to standardized test scores when students reported higher levels of conscientiousness (β =.05, p =.002). Students' extraversion and academic self‐efficacy did not moderate the relationship between teacher‐assigned grades and standardized test scores. Conclusions: Our findings indicate that students' conscientiousness is a personality trait that seems to be important when it comes to how closely mathematics teachers align their grades to standardized test scores. [ABSTRACT FROM AUTHOR]

With the technological improvements of innovative portable recording gadgets, augmented researchers' interest in exploring students' visual attention in their natural and normal occurring classrooms. The purpose of this study was to gauge students' visual attention in their Mathematics and English classrooms. This article reports on a study conducted in three schools in Santiago, Chile, where a sample of 113 randomly selected students wore a mini‐video camera mounted on eyeglass in their Mathematics and English lessons. Using Google images, we automatically and objectively examined 723,600 frames from the recordings where the classroom teacher appeared in the students' visual field. The results show that students' visual attention varies depending on four factors: (a) gender of the student, (b) age of the students, whether students are low/high attainers and (d) whether students are in English or Mathematics lessons. Surprisingly, students significantly paid more visual attention in their Mathematics than in English lessons. High attainers were more visually engaged than their low attainers counterparts. Students appeared to be visually engaged differently at different stages in their education. Furthermore, girls were more visually engaged than boys. The results of this study can have enormous practical implications for teachers and teacher education, in order to be better visually engaged with students during teaching. Lay Description: What is already known about this topic: The advantage of computers and technologies as tools in analysing teaching and learning.Measuring students' visual attention to teachers in different subject disciplines.Using first person's perspective (students' perspectives) in analysing classroom interaction. What this paper adds: Measuring students' visual attention to teachers in Mathematics and English classrooms using 723,600 frames.Students are more visually engaged to teachers in Mathematics versus English classrooms.Higher grade point average students are more visually engaged to teachers than their lower GPA counterparts.Female students significantly pay more visual attention to their teachers than their male peers.Students' visual attention to teachers is dependent on the year of study. Implications for practice and/or policy: Identifying students with lack of visual attention to the teacher objectively and automatically.Practical implications for teacher education courses, and also continuing Professional Development courses for in‐service teachers. [ABSTRACT FROM AUTHOR]

Background: Key elements of instructional quality include the teacher's ability to immediately react in domain‐specific classroom situations. Such skills – defined as action‐related skills – can only be validly assessed using authentic representations of real‐life teaching practice. However, research has not yet explained how teachers apply domain‐specific knowledge for teaching and to what extent action‐related skills are transferable from one domain to another. Aims: Our study aims to examine (1) the relationship between action‐related skills, content knowledge, and pedagogical content knowledge, and (2) the domain specificity of action‐related skills of (prospective) teachers in the two domains of mathematics and economics. Sample(s): We examined German pre‐service and in‐service teachers of mathematics (N = 239) and economics (N = 321), including n = 96 (prospective) teachers who teach both subjects. Methods: Action‐related skills in mathematics and economics were measured using video‐based performance assessments. Content knowledge and pedagogical content knowledge were assessed using established paper–pencil tests. Correlation analyses, linear regressions, and a path model were applied. Results: In mathematics and economics, we find a similar pattern of moderate correlations between action‐related skills, content knowledge, and pedagogical content knowledge. Moreover, a significant correlation between action‐related skills in mathematics and economics can be explained almost entirely by underlying relations between content knowledge and pedagogical content knowledge in both domains. Conclusions: Our findings suggest that action‐related skills empirically differ from domain‐specific knowledge and should be considered as domain‐specific constructs. This indicates that teacher education should not only focus on domain‐specific teacher knowledge, but may also provide learning opportunities for action‐related skills in each domain. [ABSTRACT FROM AUTHOR]

This paper aims at estimation of the state of the knowledge (understanding) of the individual learner by executing a test composed of a small number of items. The following approach is proposed: (1) a teacher model is introduced, and the inference process for the understanding state of the learner is represented using the Bayesian network; (2) as the network information of the items based on the teacher model, EVINI (expected value of item network information) is proposed. As the test information, EVTIN (expected value of test information with network) is proposed; and (3) a strategy for item selection based on EVINI is proposed. The following advantages are realized in practice: (1) only a small amount of data is required to construct the model; (2) the goal of inference is to know the understanding state of the individual learner, and the result provides the feedback from an educational viewpoint; (3) the knowledge of the teacher about the domain can be utilized in the inference process, which helps to improve the prediction efficiency; and (4) it is easy to add or modify the knowledge of the teacher model. In this paper, the proposed technique is applied to the real data, as the inference example of the method. The strategy for presenting the items is compared to item response theory, and discussions are made from the theoretical viewpoint. [ABSTRACT FROM AUTHOR]

Studies have shown that educational robotics (ER) may impact student learning, especially in relation to STEM (science, technology, engineering, and mathematics) areas. In the STEM framework, particularly for younger children, the "E" and the "T" are considered to be missing letters, because few studies have concentrated on teaching and evaluating technology and engineering through ER activities. This study aimed to develop and test the efficacy of an ER protocol to teach robotics in a sample of 389 students, hypothesizing that girls would be as successful as boys. A Robotics Questionnaire assessing the basics of robotics was developed for this study. A Wilcoxon nonparametric test was performed in order to evaluate improvements (p < 0.05). A Mann–Whitney nonparametric test was performed in order to test the presence of gender differences (p < 0.05). Data indicated significant improvements for all the age ranges considered. No gender differences were found. In order to evaluate the efficacy of a didactic intervention utilizing ER, it is important to assess the impact on children's technological and engineering (robotics, in particular) knowledge. Lay Description: What is already known about this topic: Studies have shown that educational robotics (ER) has a potential impact on student learning.In the STEM framework, the "E" and the "T" are considered the STEM missing letters.What this paper adds: This study aims at developing and testing the efficacy of an ER protocol to teach robotics.The hypothesis that girls will be equally successful than boys is explored too, and no gender differences were found.Implications for practice and/or policy: Our results suggest that ER can be utilized to learn robotics, bringing technology in the schools.ER could be considered as a tool able to contribute to girl's involvement in STEM. [ABSTRACT FROM AUTHOR]

Fidelity of curriculum implementation (FOI) is an important area of research because of the critical role it plays in understanding how and why curriculum materials work and how they can be improved. This analysis explores written features within the Math Trailblazers curriculum that may influence the ways teachers implement mathematics curriculum materials. In particular, we examine FOI data from prior research in order to identify features within the materials themselves that may influence why teachers adhere to the intended curriculum to varying degrees. This paper reports on our analysis of examining five whole number lessons previously analysed for level of FOI alongside an analysis scale of written curriculum features. Our purpose in this analysis is to examine features of the written curriculum that potentially mediate teachers’ implementation of the materials in line with the intended curriculum. In doing so, our analysis further emphasises the critical role teachers play in curriculum implementation, and thus may provide some insight for curriculum developers as they consider ways in which to design the written curriculum that increase the likelihood that teachers will adhere to the intended curriculum. [ABSTRACT FROM PUBLISHER]

Mathematics autobiographies have the potential to help teachers reflect on their identities as mathematics learners and to understand their role in the development of their students' mathematics identities. This paper reports on a professional development project for K-2 teachers ( n = 41), in which participants were asked to write mathematics autobiographies. Using an adaptation of an existing framework for characterizing teachers' mathematics stories, we describe the consistencies among the participants' experiences as mathematics learners and the events that are identified as being the impetus for a transition from a negative to a positive attitude toward mathematics. Implications for both teachers and teacher educators are presented. [ABSTRACT FROM AUTHOR]

In this article, we describe preservice elementary teachers 'reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers 'memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually. [ABSTRACT FROM AUTHOR]

In this article, Anies Al-Hroub, assistant professor of educational psychology and special educational needs at the American University of Beirut in Lebanon, and David Whitebread, senior lecturer in psychology and education in the University of Cambridge Faculty of Education, discuss the identification, by teachers, of children who are gifted in mathematics and who also experience reading difficulties or specific learning difficulties. The findings reported here are based on research carried out in three state schools in Jordan, and reveal the extent to which teachers accurately nominated the ‘dual-exceptional’ children studying in their classes. The paper reviews the issues and evidence relating to teacher nomination of these children and examines the quality of teacher nominations by comparing them with identification procedures using psychological and dynamic testing. Anies Al-Hroub and David Whitebread reveal that the accuracy of the teacher nominations recorded in their research was highly variable and explore a series of factors influencing the processes of teacher nomination. They argue that teacher nomination is an essential first element in the identification process and can be easily improved. The authors call for professional development for teachers in order to raise awareness and to enable them to provide support for children with complex special educational needs more effectively. [ABSTRACT FROM AUTHOR]

In spite of repealed reform efforts, there is research and data that suggest that teachers lack the needed knowledge to successfully teach elementary mathematics. Some argue that teachers lack the needed content knowledge while other argue that a lack of confidence and practice are impacting teachers `ability to successful leach mathematics. As a result of these issues, this paper looks at the impact of a service-learning experience on pre- service teachers' confidence and preparation in the area of mathematics. The service-learning experience had a number of intended and unintended outcomes. As a result of the service-learning experience. pre-service teachers noted increased understanding, innovation and confidence in the area of mathematics. [ABSTRACT FROM AUTHOR]

Sioned Exley is the SENCo at Guilsborough School, a comprehensive school with 1,300 students in rural Northamptonshire. She undertook the research reported in this paper while working towards her MA at De Montfort University. The study reported here looked at whether teaching to the preferred learning styles of students with dylexia can improve their performance and attainment. Sioned Exley worked with a sample of seven students, four boys and three girls, in Years 7 and 8 in her school. Using both qualitative and quantitative methods, she indicates that five of the seven students made significant progress in both spelling and number work. All the students, in interviews, reported improved feelings about and attitudes towards their school work. While acknowledging that this is a small-scale study, Sioned Exley draws some positive conclusions. [ABSTRACT FROM AUTHOR]

Facility with language is critical for students' academic success. In this article, we discuss the 3Ps model for planning for language use and instruction across content areas such as science, mathematics, and social studies in early childhood classrooms. Focusing on the participants, purpose, and place of communication can help teachers plan for incorporating content‐area registers across the school day. [ABSTRACT FROM AUTHOR]

This mixed methods study explored the development of elementary and middle school preservice teachers' (PSTs) learning to assess student thinking through analysis of students' written work. Six sections of the first mathematics content course for teaching implemented two writing assignments focused on analysis of student work aligned to the mathematics topics covered in the PSTs' classes. Using quantitative methodology, we examined the PSTs' (n = 99) change in their noticing and assessment skills of attending to and interpreting students' thinking. We also documented their mathematical content knowledge (MKT) as measured by the Learning for Mathematics Teaching in the domains of specialized content knowledge and knowledge of content and students. Findings show that the PSTs increased in their assessment skills and in their MKT. Using a qualitative methodology on interview data of a subset of eight PSTs, we found they acknowledged that having a firm grasp of mathematical content is essential to understanding and explaining student thinking. Findings indicate that engaging PSTs in the real work of teaching such as noticing and assessing students' thinking through written work at the early stages of their teacher preparation may motivate PSTs to learn mathematics more deeply with an eye towards strengthening their assessment skills. [ABSTRACT FROM AUTHOR]

In this article, we describe the case of "Keri," a fifth‐grade teacher who had completed an Elementary Mathematics Specialist (EMS) certification program. Drawn from a larger study investigating the knowledge, beliefs, and practices of EMSs, Keri's case was unique in that she was teaching mathematics to four classes in a departmentalized structure, where students were placed into different classes according to perceived mathematics ability. Observations from the larger study revealed that Keri's instructional practices did not align with her reported beliefs and knowledge. To explore this deviation, we conducted a case study where we observed Keri's instruction across multiple classes and used interviews to explore reasons for Keri's instructional decisions in terms of her perceived professional obligations. We found that Keri did employ practices that were aligned with her reported beliefs and knowledge such as pressing students for mathematical justifications, but only in her "higher ability" classes. Interview data suggested that Keri's decisions were driven by a strong obligation to individual students, overriding other obligations. We describe implications of these findings, including the limitations of teacher assessments and surveys as proxies for teaching quality, and discuss recommendations for approaches to teacher development that account for teachers' perceived obligations. [ABSTRACT FROM AUTHOR]

Background: Research into numerical cognition has contributed to a large body of knowledge on how children learn and perform mathematics. This knowledge has the potential to inform mathematics education. Unfortunately, numerical cognition research and mathematics education remain disconnected from one another, lacking the proper infrastructure to allow for productive and meaningful exchange between disciplines. The present study was designed to address this gap. Aim: This study reports on the design, implementation, and effects of a 16‐week (25‐hour) mathematics Professional Development (PD) model for Kindergarten to Grade 3 educators and their students. A central goal of the PD was to better integrate numerical cognition research and mathematics education. Sample: A total of 45 K‐3 educators and 180 of their students participated. Methods: To test the reproducibility and replicability of the model, the study was carried out across two different sites, over a two‐year period, and involved a combination of two different study designs: a quasi‐experimental pre–post‐research design and a within‐group crossover intervention design. Result: The results of the first implementation (Year 1), indicated that compared to a control group, both teachers and students benefited from the intervention. Teachers demonstrated gains on both a self‐report measure and a test of numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on the self‐report measure, but not the test of numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. Conclusion: The current PD model is a promising approach to better integrate research and practice. However, more research is needed to determine in which school contexts the model is most effective. [ABSTRACT FROM AUTHOR]

Mindsets have been shown to greatly influence individuals' efforts and subsequent success in the endeavors they attempt. This is particularly true of mathematical endeavors where mindset impacts the ways in which individuals approach and persevere in learning. This exploratory study investigated the mathematical mindsets held by 242 prospective teachers in undergraduate mathematics content courses for PreK‐8 teachers as well as examined the relationships between mindset, depth of learning, challenge seeking choices, and course grades. A strong predictive nature was found to exist among these variables. Recommendations are identified for future research to investigate prospective teachers' mindsets and depth of learning. [ABSTRACT FROM AUTHOR]

Abstract This paper explores the nature of Information Technology (IT) as a separate subject in the secondary school curriculum. It reports on research carried out with a cohort of specialist IT post-graduate trainee teachers at a local university. The paper explores IT trainees' approach to teaching their subject and describes their strong focus on purpose when teaching IT. Important characteristics of the purposeful approach are the use of authentic data; the transformation of data by pupils; and a focus on problem solving within a context to which pupils can relate. However in their work in schools, trainees found constraints on developing a strong focus on purpose in their lessons. They were encouraged to experiment but felt they needed more support to carry out purposeful activities with pupils. The implications of this research on teacher training and on the value of IT as a curriculum subject are discussed. [ABSTRACT FROM AUTHOR]

Given the increasing diversity of the student body, teachers are called to appropriately address students' various learning needs by means of differentiated instruction (DI). However, empirical research has yielded mixed evidence on teachers' reported use of DI. Using nationally representative data from the National Educational Panel Study in Germany, this article aimed to explore German (as native language) and Mathematics teachers' use of DI practices. In addition, this study took into consideration contextual factors, such as school track, and investigated the impact of teachers' constructivist beliefs on their DI implementation. Results from a mixed analysis of covariance indicated that teachers occasionally implement DI practices. Furthermore, between‐subject effects reported differences across school tracks. It appears that advanced secondary school teachers implement less often DI practices. The covariate of teachers' constructivist beliefs was also positively linked to overall teachers' implementation of DI. Implications of the results, as well as further lines of research are discussed. [ABSTRACT FROM AUTHOR]

Elementary standards include multiplication of single‐digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning provides the foundation for advanced mathematics and algebraic reasoning. For students who struggle in mathematics, instruction in multiplication algorithms should ensure conceptual understanding so that students have a foundation for success in advanced mathematics. The concrete representational abstract (CRA) sequence addresses conceptual understanding and the strategic instruction model (SIM) supports procedural knowledge. The current pilot study combined these methods to teach elementary students the partial products algorithm. Twelve students in grades four and five participated in the study, receiving instruction from teachers in their school during an intervention period. Within a pre‐experimental design, using pre‐ and postintervention data, students showed a significant change in performance. The article will describe and show how teachers implemented the CRA‐SIM interventions and discuss implications for practice. [ABSTRACT FROM AUTHOR]

Objectives: Children's additional health and developmental needs are often first identified by teachers when they begin school. This study estimates the Grade 3 literacy and numeracy outcomes of children with teacher‐identified additional needs emerging in the first year of school, including the added burden conferred by socioeconomic disadvantage. Methods: Population linked data (n = 42,619) were analysed from the Australian Early Development Census, which include teacher reports on children's health and development at school entry, and the National Assessment Program–Literacy and Numeracy, a direct assessment of reading and numeracy skills at Grade 3. Linear regression analyses were used to estimate associations between emerging needs and learning outcomes, adjusted for sociodemographic characteristics. The combined effect of emerging needs and low maternal education (an indicator of socioeconomic disadvantage) on academic outcomes was examined by estimating the relative excess risk due to interaction (RERI). Results: Emerging health and developmental needs at school entry were associated with lower reading (b = −26.86, 95% CI = −29.19, −24.52) and numeracy (b = −24.39, 95% CI = −26.43, −22.35) outcomes at Grade 3. The combined effect of emerging needs and socioeconomic disadvantage was greater than expected when their individual effects are summed (RERI = 0.38, 95% CI 0.22, 0.55 for reading and RERI = 0.27, 95% CI 0.10, 0.43 for numeracy). Conclusion: In the current study, emerging health and developmental needs identified by teachers at the outset of schooling were associated with poorer literacy and numeracy skills at Grade 3, and family socioeconomic disadvantage appeared to further amplify this effect. Meeting the needs of these children will require timely and coordinated supports across the health and education systems, particularly for those children who are also disadvantaged. [ABSTRACT FROM AUTHOR]

Recent research on teachers' use of student mathematical thinking (SMT) and recommendations for effective mathematics instruction claim that how teachers respond to SMT has great impact on student mathematical learning in the classroom. This study examined some Chinese mathematics teachers' responses to student in‐the‐moment mathematical thinking that emerged during whole class discussion. The findings of this study revealed that the majority of Chinese elementary mathematics teachers in the data involved the whole group of students to make sense of in‐the‐moment SMT. They either invited students to digest SMT involved in the instance or provided an extension of the instance to further develop student mathematical understanding. [ABSTRACT FROM AUTHOR]

Background: Tasks that involve retrieving information from memory, such as answering short answer questions, are more effective at improving learning than restudying, concept mapping, and other study techniques. However, little is known about how often teachers naturally provide these retrieval practice opportunities during lectures and classroom discussions. Aims: To identify how often teachers ask questions that require retrieval, what types of retrieval questions they ask, and whether teachers in high‐growth classrooms differ in their use of retrieval questions compared to teachers in low‐growth classrooms. Sample: The sample included twenty middle school mathematics classrooms that showed high growth on a test of mathematics achievement and twenty with low growth. For each classroom, we examined a videotape of one class period. Methods: We coded the number of teacher questions in each lesson, and the number and type of questions that provided an opportunity for retrieval. Results: We found wide variability in the frequency and type of questions asked across classrooms. On average, almost half of the non‐classroom management questions provided an opportunity for retrieval. However, teachers in high‐ and low‐growth classrooms asked similar numbers and types of retrieval questions. Conclusions: Teachers naturally use a wide variety of retrieval questions in their mathematics classrooms. As such, improving their use of retrieval opportunities will require only small changes to their natural practice, rather than large changes to their instructional style. [ABSTRACT FROM AUTHOR]

In this study, we explored the extent to which teachers agree on the ordering and separation of levels of two different learning progressions (LPs) in English language arts (ELA) and mathematics. In a panel meeting akin to a standard‐setting procedure, we asked teachers to link the items and responses of summative educational assessments to LP levels. We evaluated four types of agreement among teachers, with test developers, and with trained raters. Although the results were quite mixed, agreement on the LP levels of mathematics items was generally better than that for ELA tasks. The agreement on the LP levels of ELA sample responses was generally better than that for mathematics. Implications of the results are discussed. Report Number: ETS RR–18‐11 [ABSTRACT FROM AUTHOR]

Abstract: The study was situated in a National Science Foundation supported Math Science Partnership between a private university and an urban school district. This study sought to understand the decision‐making process of elementary teachers as they implement an integrated science, technology, engineering, and mathematics (STEM) curriculum in their classrooms and the interactions that occur between the teachers and curriculum during that process. This qualitative study utilized a comparative case study approach to understanding the decision‐making process of three elementary teachers enacting the same lesson. Analysis of the interactions revealed that the teachers' perceptions of student ability, their pedagogical design capacity, and time were influences that impacted implementation. These findings have implications for STEM‐focused professional development of elementary teachers. [ABSTRACT FROM AUTHOR]

Abstract: As more attention is placed on designing digital educational games to align with schools' academic aims (e.g., Common Core), questions arise regarding how professional development (PD) may support teachers' using games for instruction and how such integration might impact students' achievement. This study seeks to (a) understand how teachers use PD resources (e.g., technology personnel and game‐use workshops) for integration; (b) determine how teachers integrate games into their instruction; and (c) examine how those teaching practices are associated with student achievement. This mixed method study used survey and interview responses from elementary school teachers (n = 863) with access to PD resources for implementing a math game intervention and standardized math‐test scores from their second‐ through sixth‐grade students (n = 10,715). Findings showed few teachers sought PD assistance for integration, but many desired such support. Some reported using integrative practices (i.e., referencing game and using game‐generated progress reports) to identify struggling students, whereas several found integration challenging. Teachers' reordering of game objectives to align with lessons and viewing of game‐based PD videos were associated with increased student math achievement in our OLS‐analysis. However, this result was no longer statistically significant within a school fixed‐effects model, suggesting school differences may influence how strongly teachers' practices are associated with student achievement. [ABSTRACT FROM AUTHOR]

The practices of effective primary school teachers including students with Down syndrome in their mathematics classes are largely unexplored and many teachers feel unprepared to teach students with an intellectual disability. The authors sought to find out what these specific professional learning (PL) needs were and if they changed over time. A mixed methods study was undertaken to investigate the practices of primary mathematics teachers including students with Down syndrome in regular class lessons in two Australia educational jurisdictions. A variety of approaches was used to gain an understanding of their practices. Findings are based on responses to a questionnaire administered to teaching teams at the beginning and end of the school year. There was a strong endorsement of inclusion as an appropriate practice in primary mathematics. The PL needs of teaching teams changed across the teaching year. Early requirements concerned understanding Down syndrome and its impact on learning and behavior. As the school year progressed, PL needs changed toward a greater focus on the need for specific resources and strategies for teaching mathematics. The PL requirements of teachers included the need for 'in-time' support. The authors conclude that even if it may be infrequent when a teacher has a student with Down syndrome in a mathematics class, teachers still need access to PL that evolves across the school year, from less focus on syndrome-specific information to greater emphasis on teaching mathematics through adjusting learning outcomes and teaching approaches. [ABSTRACT FROM AUTHOR]

Background: Working memory deficits have been found for children with specific language impairment (SLI) on tasks imposing increasing short-term memory load with or without additional, consistent (and simple) processing load. Aims: To examine the processing function of working memory in children with low language (LL) by employing tasks imposing increasing processing loads with constant storage demands individually adjusted based on each participant's short-term memory capacity. Methods & Procedures: School-age groups with LL ( n = 17) and typical language with either average ( n = 28) or above-average nonverbal intelligence ( n = 15) completed complex working memory-span tasks varying processing load while keeping storage demands constant, varying storage demands while keeping processing load constant, simple storage-span tasks, and measures of language and nonverbal intelligence. Teachers completed questionnaires about cognition and learning. Outcomes & Results: Significantly lower scores were found for the LL than either matched group on storage-based tasks, but no group differences were found on the tasks varying processing load. Teachers' ratings of oral expression and mathematics abilities discriminated those who did or did not complete the most challenging cognitive tasks. Conclusions & Implications: The results implicate a deficit in the phonological storage but not in the central executive component of working memory for children with LL. Teacher ratings may reveal personality traits related to perseverance of effort in cognitive research. [ABSTRACT FROM AUTHOR]

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress ( NAEP). A set of eight instructional modules was developed and tested. The study involved 7 university instructors and 542 preservice teachers ( PSTs) from three different universities. A quasi-experimental nonequivalent groups design was used for this study in which the following data sources were collected and analyzed. Three versions of a Learning Mathematics for Teaching test were given to assess PSTs' mathematical content knowledge for teaching: (a) Elementary Number Concepts and Operations- Content Knowledge; (b) Elementary Geometry- Content Knowledge; and (c) Middle School Number Concepts and Operations- Content Knowledge. In addition, the Mathematics Teacher Efficacy Beliefs Instrument was given to assess PSTs' teacher efficacy beliefs. Test results were analyzed using paired samples t-tests. Findings suggest that use of instructional materials, based on NAEP, with PSTs results in increases in their mathematical content knowledge for teaching and in their teaching efficacy beliefs. [ABSTRACT FROM AUTHOR]

Starting on positive trajectories at school entry is important for children's later academic success. Using partial least squares, we sought to specify interrelations among all theory-based components of social-emotional learning (SEL), and their ability to predict later classroom adjustment and academic readiness in a modelling context. Consequently, self-regulation, emotion knowledge, social problem solving, and social-emotional behaviour were assessed via direct assessment and observation for 101 preschoolers; teachers provided information on classroom adjustment through kindergarten and academic readiness in kindergarten. Our final outer (measurement) model showed robust latent variables for SEL components. Regarding the inner (structural) model, latent variables showed expected predictive relations among SEL components, and with later classroom adjustment and academic readiness: preschoolers' executive control predicted aspects of their social cognition (i.e., emotion knowledge and social problem solving) and emotionally negative/aggressive behaviour, and emotion knowledge predicted their emotionally regulated/prosocial behaviour. Further, most SEL components directly and/or indirectly predicted teachers' evaluations of later classroom adjustment and kindergarten academic readiness. Our findings extend our understanding of SEL during preschool, suggesting that early assessment and monitoring is possible using these instruments, and potentially aiding the development of programmes to maximize children's SEL in the service of early school success. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills are built. The purpose of this study is to recognize indicators of multiplicative reasoning among fourth-grade students. Through cross-case analysis, the researcher used a test instrument to observe patterns of multiplicative reasoning at varying levels in a sample of 14 math students from a low socioeconomic school. Results indicate that the participants fell into three categories: premultiplicative, emergent, and multiplier. Consequently, 12 new sublevels were developed that further describe the multiplicative thinking of these fourth graders within the categories mentioned. Rather than being provided the standard mathematical algorithms, students should be encouraged to personally develop their own unique explanations, formulas, and understanding of general number system mechanics. When instructors are aware of their students' distinctive methods of determining multiplicative reasoning strategies and multiplying schemes, they are more apt to provide the most appropriate learning environment for their students. [ABSTRACT FROM AUTHOR]

Teachers constantly question their own practice. Often, their questions remain unexplored. Collegial observation provides one way to see teaching differently and understand the tensions involved in incorporating new theoretical understandings into practice. Gebhard (1999) argues that conversations preceding and following such observations are critical triggers for teacher development. The questions, conversations, and observations that are the focus of this article occurred within a larger case study with teachers who taught culturally and linguistically diverse classes comprising students who were native English speakers as well as students who spoke English as an additional language. Pairs of secondary content teachers (social studies, science, and mathematics) planned, implemented, and evaluated lesson sequences with a language focus in their content area. Each pair chose one principle from language learning research to guide the design of their sequence. This article investigates the mathematics pair's use of collegial observation to explore ways of incorporating opportunities for student interaction, particularly for English language learners, in their lesson sequence. Findings suggest that such observations and conversations contribute to understanding the tensions in questioning, seeing, reimagining, and reshaping practice. What makes this observation so unusual is that New Zealand secondary schools lack a systemic collegial culture. [ABSTRACT FROM AUTHOR]

In Florida, recent legislative changes have granted community colleges the ability to offer baccalaureate degrees in education, frequently to non-traditional students. Based on information obtained from the literature covering preservice teachers' math knowledge, teachers' efficacy beliefs about math, and high-stakes mathematics testing, a study examined a population of preservice teachers in a new Florida teacher preparation program. The research investigated relationships surrounding non-traditional preservice teachers' characteristics such as: ages, high-stakes math failures, lower division mathematics history, and math methods course performance, in relation to their efficacy beliefs about mathematics. Results revealed that preservice teachers' ages, lower division mathematics history, and math methods course performance, did have a significant relationship with their math efficacy beliefs, as measured by the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI); the variable of high-stakes math failures did not. Additionally, a multiple regression model including the aforementioned variables did predict preservice teachers' MTEBI scores, but did not generalize to the greater population. The findings from this study can assist new teacher preparation programs in isolating variables that identify preservice teachers who are at risk for poor mathematical attitudes; can posit avenues for fostering positive math beliefs in preservice teachers; and can recommend further research in this area. [ABSTRACT FROM AUTHOR]

With inquiry being one of the central tenets of the national and most state standards, it is imperative that we have a solid means to measure the quality of inquiry-based instruction being led in classrooms. Many instruments are available and used for this purpose, but many are either invalid or too global. This study sought to compare two observational protocols: Electronic Quality of Inquiry Protocol (EQUIP) and Reformed Teacher Observation Protocol (RTOP) with regard to reliability, validity, and utility associated with inquiry-based instruction. Analyses included studying item reliability, inter-rater reliability, factor analysis, correlation, and multiple regression of protocol items within the instruments and between the instruments. General findings suggest that both instruments have high item reliability and are effective measures in both math and science classrooms; EQUIP showed higher inter-rater reliability and seems to be more valid for measuring inquiry-based instruction, while RTOP seems better suited for looking more globally at constructivist teaching practices. Additionally, the utility of EQUIP seems to be larger. It is useful for looking formatively at individual teaching practice, as well as studying summative teacher growth or program effectiveness. Further, because EQUIP uses a descriptive rubric instead of a Likert scale, the instrument provides immediate and targeted feedback to teachers, instructional leaders, and professional development facilitators. This feedback includes both a micro view (individual indicators) and a macro view (construct) of teaching practice. [ABSTRACT FROM AUTHOR]

Using data from 503 inservice elementary teachers, this study investigated the relationship between teachers' background characteristics, teachers' beliefs about manipulatives, and the frequency with which teachers use manipulatives as part of their mathematics instruction. Findings from the study show that teachers' grade level and beliefs about manipulatives are important predictors of teachers' use of manipulatives in their mathematics instruction. [ABSTRACT FROM AUTHOR]

Previous research (e.g., Woodward & Baxter 1997) found that Standards-based mathematics teaching provides. marginal or no benefits for low achievers, in contrast with positive effects for middle and high ability students. A randomized quasi-experiment in 52 Canadian schools found that low achieving grade 7 and 8 students who received support consisting of placement on a learning continuum, instruction focused on their specific learning needs, and concrete materials to represent mathematical constructs, benefited from teaching that emphasized construction over transmission of knowledge. Treatment students showed small but statistically significant improvements over controls in student achievement, and controversially, in mathematical beliefs, and attitudes. The latter finding raised issues of the appropriate balance between Type I and Type II error in educational research. [ABSTRACT FROM AUTHOR]

Classroom tests from nine eighth-grade mathematics teachers were collected from the 2003-04 and 2005-0 6 school years. These years represent one school year prior to the eighth-grade Ohio Achievement Test (OAT) in mathematics being implemented and the year after the eighth-grade OAT in mathematics was implemented, respectively. In addition, teachers were interviewed to determine factors that influence classroom assessment practices. Classroom assessment data were compared between the two years, and interview data were examined, to investigate the impact that the new state test was having on classroom assessment practices. An average of 87% of teachers `classroom assessment items were at the lowest depth of knowledge level during both years. Teachers relied heavily on curriculum materials for their test items, and these items tended to only assess students ability to recall basic facts or perform straightforward procedures. The presence of a state test did not entice teachers to assess students at higher depth of knowledge levels. [ABSTRACT FROM AUTHOR]

Non-traditional forms of instruction provide exciting and engaging opportunities for mathematics education. This article proposes the use of mathematical figures painted on the school playground as an environment to support mathematical teaching, learning, and understanding. Teachers plan mathematics lessons to take advantage of the playground figures and present new topics, reinforce current topics, and review previous topics. Figures were chosen to support mathematical concepts required by the curriculum and state and national standards. The intentional blank portions of the playground figures allowed for adjustment of lesson activities to meet different grade level and individual student needs, as well as making the figures interactive with the use of sidewalk chalk. A teacher handbook suggests activities for each figure by grade level, and teachers often create their own ideas for using the figures. Students like the change of perspective and teachers feel that such lessons help to raise standardized test scores because the information is better retained. The lessons addressed multiple learning styles, help with vocabulary for English Language Learners, and infuse higher thinking levels into lessons. [ABSTRACT FROM AUTHOR]

This study examines the beliefs of K-8 preservice teachers during a content methods course. The goals of this course included exposing the preservice teachers to student-centered instructional methods for math and science and encouraging the development of lessons that would integrate mathematics and science. Prior research suggested that one must consider preservice teachers 'epistemic beliefs (Cady, Meier, & Lubinski, 2006a) as it influences their interpretation of the teacher education program. In this study, preservice teachers 'epistemic beliefs were identified, their beliefs about mathematics and science teaching and learning were identified and compared, and their descriptions of lessons that integrated mathematics and science were assessed. Findings suggest that preservice teachers made decisions based on an external locus of control and harbored greater anxiety about teaching math as compared to teaching science. They also indicate that the integration of mathematics and science in lesson plans was contrived. [ABSTRACT FROM AUTHOR]

Teacher judgments have been identified as a primary source of information regarding student academic achievement. Research examining the accuracy of teachers' judgments in assessing students' academic abilities has shown relatively high accuracy. However, previous studies have relied primarily on norm-referenced measures to obtain estimates of students' achievement in reading and mathematics. Recent developments in the assessment of students' academic skills, such as Curriculum-Based Measurement (CBM), provide a direct estimate of students' skill levels in basic areas such as reading and mathematics. The purpose of the present study was to examine the extent to which teachers' perceptions of students' reading and mathematics skills corresponded to direct estimates of students' reading and mathematics skills. Two second-grade teachers estimated the reading and mathematics skills of 33 second-grade students. Results of this study indicated that teachers were not accurate in assessing their students' mathematics functioning. Teachers were more accurate in assessing the occurrence of Mastery mathematics levels in basic addition, but were very inaccurate in assessing the occurrence of Mastery, Instructional, or Frustrational mathematics levels in all other skills assessed. In reading, teachers' judgment accuracy varied as a function of grade-level material and instructional level. Specifically, teachers experienced considerable difficulty accurately identifying students who were reading at a Mastery level in grade-level or above-grade-level material. © 2006 Wiley Periodicals, Inc. Psychol Schs 43: 247–265, 2006. [ABSTRACT FROM AUTHOR]

Preservice teachers in a bachelor of education (Primary and ECE) program were surveyed about their beliefs and attitudes toward mathematics and its teaching and learning, at the beginning of their first mathematics curriculum unit and again at the end of their second mathematics education unit, approximately 18 months later. Significant differences were found for several items. However, in comparison to previously noted changes in the beliefs of similar cohorts from the beginning to end of a single unit, the changes were relatively 'small. Aspects of the course that students considered valuable and which may have contributed to the changes are also reported. [ABSTRACT FROM AUTHOR]

The article reports on the findings of a survey conducted to determine which science, engineering, and math (SEM) majors during which years in their undergraduate education and from which academic performance levels are most interested in K-12 teaching. In the United States, there is a serious shortage of qualified math and science teachers. Troubled not only by recruitment, the science and math K-12 teaching field also suffers from flagging retention. Only 4% of new math and science teachers report foreseeing teaching as a longer-term career commitment. One result of the supply shortage of K-12 science and math teachers is the field's reported decline in content knowledge preparation. Nearly 32% of math and science teachers report majoring in neither math nor science. When disaggregated by discipline at the high school level, as of 1999, those without majors in their subject areas number 37% of biology teachers, 59% of physical science teachers, and 60% of math teachers. These unpromising statistics grow more extreme in middle schools and high-poverty public high schools, especially regarding math and physical sciences instruction.

Integration of content in core disciplines is viewed as an important curricular component in promoting scientific literacy. This study characterized the current practices of a group of elementary teachers relative to their development of interdisciplinary links between science, mathematics, and literacy. A qualitative analysis of survey data showed that there were substantial differences in the use of a well-developed process for integrating instruction. Teachers also lacked a conceptual connection to integration, showed contradictions in the importance placed on hands-on experiences, used measurement as the primary interdisciplinary connection between mathematics and science, and did not use instructional strategies designed specifically for nonfiction/ expository text. The findings underscore the need for professional development that assists teachers in changing their conceptual perspectives to integration while also building pedagogical knowledge related to integration of science, mathematics, and literacy. [ABSTRACT FROM AUTHOR]

Increasingly, the mathematical subject knowledge required of teachers is described as lists of facts, skills and competencies. This listing appears unproblematic given the apparently rational nature of the subject. However, mathematics is often experienced as an intensely emotional subject. The focus of this article is shame: a reaction to other people's criticisms and an emotional response to knowing and doing mathematics. It is used as an analytical tool to explore the ways in which mathematics is known by primary school teachers. It is suggested that absolutist/product conceptions of mathematics provide ideal opportunities for experiencing shame and that, while shame can act as a positive motivational force, accessing it in this way is far from easy. [ABSTRACT FROM AUTHOR]

Presents information on a study which examined teachers' conceptions about assessment practices in mathematics education. Description of research methods used in the study; Examination of statistical data on teachers' assessment practices; Results of this research.

This article describes how an elementary teacher of mathematics and science perceived a problem with the curriculum, confronted the constraints, and established an environment conducive to learning with understanding. The authors conducted an interview with the teacher's friends, students and parents in order to obtain the data for this issue. In addition, the teacher's class was also been observed. The article also overviews the teacher's story, which emphasize her growth, development and commitment to the goal facilitating learning through materials centered activities in science and mathematics.

The article presents a case study on the practices of outstanding science and math teachers . The authors assert that much could be learned from case studies from the best science and mathematics teachers. Also,they believed that such case studies of exemplary practice could lead to improvements in science and mathematics teaching by motivating and guiding teachers’ attempts to improve their practice. They conducted intensive classroom observations of teachers who were nominated and invited to participate in the study.